Interior-point methods handle nonlinear programs by sequentially solving barrier subprograms with a decreasing sequence of barrier parameters. In practice, adaptive barrier updates have been shown to lead to superior performance. In this talk we interpret the adaptive barrier update as a reinforcement learning task and train a deep Q-learning to solve it. Numerical results based on an implementation within the nonlinear programming solver WORHP show that the agent successfully learns to steer the barrier parameter and additionally improves WORHP's performance on the CUTEst test set.
joint work with M. Paul Laiu
A framework for accommodating infeasible starts, given a user-supplied feasible-start "base" iteration for CQP, is proposed and analyzed. Requirements to be satisfied by the base iteration allow for inexact computation of search directions. The framework is applied to a recent feasible-start "constraint-reduced" MPC algorithm, involving a small "working set" of constraints, updated at each iteration. In early numerical tests with Matlab/CVX, a speedup of up to 10x over SDPT3/SeDuMi was observed, on both randomly generated and data fitting problems with many more constraints than variables.
joint work with Stefania Bellavia, Jacek Gondzio
We address the solution of semidefinite programming (SDP) problems in which the primal variable X is expected to be low-rank at optimality, a common situation in relaxations of combinatorial optimization (maximum cut) or in matrix completion. SDPs are solved efficiently using interior-point methods (IPMs), but such algorithms typically converge to a maximum-rank solution. We propose a new IPM approach which works with a low-rank X and gradually reveals the optimal (minimum) rank. Preliminary results show that using alternating directions improves the efficiency of the linear algebra.